Magnetic properties of transition-metal nitrides
Walter R. L. Lambrecht, M. S. Miao, and Pavel Lukashev
Citation: Journal of Applied Physics 97, 10D306 (2005); doi: 10.1063/1.1846612
View online: http://dx.doi.org/10.1063/1.1846612
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JOURNAL OF APPLIED PHYSICS 97, 10D306 共2005兲
Magnetic properties of transition-metal nitrides
Walter R. L. Lambrecht,a兲 M. S. Miao, and Pavel Lukashev
Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079
共Presented on 9 November 2004; published online 5 May 2005兲
The structural stability of transition-metal nitrides 共TMN’s兲 and their magnetic properties in
different phases are investigated using first-principles calculations. The early TMN, ScN–CrN, are
found to have rocksalt as equilibrium structure at ambient pressure while the later ones 共MnN, FeN,
and CoN兲 prefer zincblende. However, the early ones can also adopt the zincblende structure under
tensile strain. The tendency towards magnetism is stronger in the rocksalt phase than in the
zincblende phase. Antiferromagnetic versus ferromagnetic ordering in the different phases and the
relevance of the results to TM-doped GaN are discussed. © 2005 American Institute of Physics.
关DOI: 10.1063/1.1846612兴
Transition metals form a wide variety of interesting
compounds with nitrogen. For any given transition metal,
there are several known crystallographic phases with different N content. Several of these have interesting magnetic
properties. Here we focus on mononitrides. While the early
nitrides all have the rocksalt 共RS兲 or a closely related structure, there have been a few reports that the later ones such as
FeN and CoN have the zincblende 共ZB兲 structure.1,2 This is
possibly interesting for making high-quality metallic contacts to semiconductors and could even be more interesting if
these compounds were also magnetic because they could
then serve as spin-injection materials. More details on FeN
and CoN are given in Refs. 3 and 4.
Doping of GaN with transition metals 共TM’s兲 such as
Mn and Cr is currently pursued to achieve dilute ferromagnetic semiconductors.5–7 However, there is increasing evidence that the observed magnetic behavior of these materials
is at least in part due to unknown precipitates.8–10 Since
MnN and CrN are known to be antiferromagnetic, they are
usually not considered as candidate magnetic impurity
phases. However, it is not clear whether the magnetic ordering of these phases could become ferromagnetic for small
particles under strain, which may even have a different crystal structure. In fact, the above trend with atomic number
suggests that a larger lattice constant or tensile strain may
favor zincblende. Clearly a better understanding of the
transition-metal nitride 共TMN兲 structural preference and
magnetic properties as a function of lattice constant is desirable.
The computational method used in this work is the localdensity-functional theory11,12 combined with a full-potential
linear muffin-tin orbital method.13 Well-optimized basis sets
and converged Brillouin-zone integrations using typically an
8 ⫻ 8 ⫻ 8 mesh are used. Additionally, to compare the small
energy differences between different crystal structures,
equivalent k-point sets are used.
Figure 1 shows the equilibrium lattice constants and the
minimum energies for ZB and RS structures as a function of
atomic number. Clearly, the early transition metals prefer the
a兲
Electronic mail: walter.lambrecht@case.edu
0021-8979/2005/97共10兲/10D306/3/$22.50
RS, the later ones the ZB phase with the crossover occurring
at MnN. The lattice constant of the ZB structure is always
significantly larger than that of the RS structures. Figure 2
shows the energy difference between RS and ZB as a function of the lattice constant for a series of TMN. It shows that
above a certain lattice constant the ZB always becomes favored.
The finding that the ZB structure has the global minimum for MnN is surprising since this phase has not been
observed experimentally. MnN1−␦ with ␦ ⬇ 0 is known to
have a slightly tetragonally distorted RS structure, known as
the ␪ phase. Preliminary calculations with 16 atom supercells
FIG. 1. Minimum-energy lattice constant and cohesive energy for ScN, TiN,
VN, CrN, MnN, FeN, and CoN in both NaCl and ZB structures.
97, 10D306-1
© 2005 American Institute of Physics
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10D306-2
J. Appl. Phys. 97, 10D306 共2005兲
Lambrecht, Miao, and Lukashev
FIG. 2. Energy difference ERS − EZB between rocksalt and zinc blende as a
function of the lattice constant for transition-metal nitrides.
indicate that the introduction of N vacancies stabilizes the
RS relative to the ZB phase.14
Figure 3 shows the magnetic moments in the RS and ZB
phases for a ferromagnetic spin-polarized calculation. We
note that the RS phase has a much stronger tendency towards
magnetism than the ZB phase. For instance in RS FeN has a
FIG. 4. Energy difference between different AFM states and the FM state
for both MnN and CrN in a RS structure and at different lattice constants.
high magnetic moment, while in ZB it only becomes magnetic at very large lattice expansion and CoN stays nonmagnetic in ZB. MnN also becomes magnetic in ZB above a
certain minimum lattice constant, while CrN has a gradually
increasing magnetic moment as a function of the lattice constant. VN shows a very weak magnetism and TiN and ScN
are nonmagnetic.
The magnetic ordering in these compounds is rather
complex. We have studied various possible antiferromagnetic
orderings as well as the ferromagnetic ordering. Specifically,
we consider antiferromagnetic 共AFM兲-关001兴1, meaning spins
align in 共001兲 planes but the spin direction flips every layer,
AFM-关111兴1, AFM-关110兴2, and so on. We note that AFM关001兴1 is equivalent to AFM-关110兴1 and that the AFM-关110兴2
ordering is known to occur in CrN, while AFM-关001兴1 occurs in ␪ MnN. In Fig. 4 we show the energy difference
between two different AFM orderings from the FM one for
MnN and CrN. Clearly MnN and CrN behave rather differently. While the experimentally observed AFM-关110兴2 ordering in CrN at the equilibrium lattice constant is connected
with an orthorhombic strain distortion, we see here that it
also occurs without this distortion at increased lattice constant. For MnN, on the other hand, this ordering is clearly
unfavorable. From mapping these energy differences and
those of other magnetic configurations to a Heisenberg
model with first and second nearest-neighbor interactions,
H=−
兺 JmnSmSn ,
具mn典
共1兲
we can extract exchange parameters. In fact, we have for
instance
EFM = 6J1 − 3J2 ,
EAFM−关001兴1 = 2J1 − 3J2 ,
共2兲
EAFM−关111兴1 = 3J2 ,
EAFM−关110兴2 = J2 ,
FIG. 3. Magnetic moments in VN, CrN, MnN, FeN, and CoN as a function
of the lattice constant for RS 共top兲 and ZB 共bottom兲.
and thus from fitting the energy differences of the various
AFM configurations from the FM phase, to these equations,
we can obtain15,16
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10D306-3
J. Appl. Phys. 97, 10D306 共2005兲
Lambrecht, Miao, and Lukashev
The occurence of the ZB phase under expansion for CrN
and MnN indicates that lattice matched ZB-phase precipitates of these materials in GaN may be favorable and could
occur in Mn- or Cr-doped III-N. Furthermore at a lattice
constant of 4.50 Å, ZB CrN prefers a FM alignment. We
suggest that ZB-phase nanosize precipitates could be responsible for the observed ferromagnetic hysteresis behavior in
Cr-doped III-N. For Mn doping it is not as clear since even
ZB particles are found to be antiferromagnetic. However,
higher Mn content compounds such as Mn4N, which is ferrimagnetic, should be considered.
FIG. 5. Energy difference between different AFM states and the FM state
for both MnN and CrN in a ZB structure and at different lattice constants.
This work was supported by the Office of Naval Research 共under Grant No. N00014-02-1-0880兲 and the National Science Foundation 共under Grant No. ECS-0223634兲.
1
J1 = − 9 meV,
J2 = 34 meV
J1 = − 9 meV,
J2 = 4 meV
for MnN,
共3兲
for CrN.
Interestingly, J1 is almost the same for these two materials.
This makes sense because it arises from the direct antiferromagnetic exchange between t2g orbitals, and the lattice constants for MnN and CrN are very close to each other. On the
other hand, J2 arises from double exchange via the N2p and
TM eg orbitals. The lower d-band filling and lower magnetic
moment in CrN means that fewer electrons contribute to this
interaction.
The energy differences of AFM-关001兴1-FM and AFM关111兴1-FM are shown in Fig. 5 for MnN and CrN. For MnN,
we find that near the minimum lattice constant the system
has zero magnetic moment. As the lattice constant expands it
becomes first AFM-关001兴1 and then AFM-关111兴1. In CrN, on
the other hand, we find that the FM state is preferred in the
ZB phase. However, looking at the two different AFM
phases, we again see a preference for AFM-关111兴1 at larger
lattice constants. This means that the exchange parameters
are functions of the lattice constant as well as of the lattice
structure.
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